APNAP is an acronym that stands for Active Player, Non-active player. It describes what happens when multiple triggered abilities trigger at approximately the same time. When they trigger does not matter as much as when they try to go on the stack. As pointed out on Monday, triggered abilities can happen at any time. And it is possible for many to trigger in-between when a player last received priority and when one will receive it again.
Active Player, Non-active Player means that when there are multiple triggered abilities that are all trying to go on the stack at one time those controlled by the active player go on the stack first, followed by those controlled by the non-active player. If a single player controls more than one triggered ability, they go on the stack in the order that he or she chooses. Because of the way the stack works, those items on the top of the stack will resolve first. This means that triggers controlled by the non-active player will resolve first. If this happen in a multiplier game, triggers go on the stack according to turn order with the active player putting his triggers on the stack first followed by those controlled by the player whose turn is next. (Extra turns generated by effects are not factored in.)
For example, if the active player controls a Fangren Marauder and the non-active player controls a Magnetic Mine, both abilities will trigger when an artifact controlled by the active player is destroyed. As the Magnetic Mine trigger is controlled by the non-active player it will go on the stack last and resolve first. This can matter, especially if the active player has a life total of two or less. If that is the case he or she will lose the game before they can gain life from the Maurader’s trigger.
Now imagine the same situation as above, but five artifacts controlled by the active player are destroyed at one time when a Creeping Corrosion resolves. In this instance, each player has five triggers to put on the stack. Technically speaking, these two player can choose the order that their triggers go on the stack but as they are all the same order does not matter. But the non-active player’s triggers will go on the stack and resolve first. If the active player’s life total is 10 or less, he will end losing the game before he gains any life.